I think that I could squeeze more points out of the bidding war by accepting bids for lower ranks after the bidding on 1st place was finished. Has anyone tried anything like that? How did it go?
You raise an interesing point, and one that I've thought about on occasion. I think the value of 3rd place (for example) may come down to whether the GM puts a greater value on ranks or points.
If the GM values ranks, then 3rd (at any cost) is just below 2nd, but if the GM values points (as I do) then 3rd may be points wasted. For example, if the top score was 44 and the second score was 42, then a 3rd place score of 15 might be points wasted because 15 is so much less than 44 that you might as well have stuck with "Amber" level instead.
It also comes down to how competitive vs cooperative the Amber campaign is run. For example, my players tend to enjoy games where they cooperate against an external foe so their exact rank doesn't matter so much. How they compare to each other comes in second to how they compare to the badduns I throw at them.
Most games are much more competitive and encourage player to player confllict. So, I guess your question is whether it is advantageous to be high in everything without being best at anything. I think the answer there would come down to how high the winner drives the bidding. If each attribute is bid so high as to totally drain the winner's points (and I assume that 2nd was nearly as high) than 3rd could be a nice deal after all.
I like to bid in order to agitate others. If I can get a cheap first rank then great! But if I can convince two people to fight tooth and nail for first and second, while leaving me with a third rank that nobody below me will ever want to buy past (because of the immense gap between third and first) even better.
But, yeah, that depends on the GM paying attention to ranks, rather than points. If the points are what matters then there is much less strategy in the auction. It's not like you can get a bargain for your points ... all you can do is manipulate what other people buy.
The GM can say he values ranks over points, but when going up against NPC's what is there? They weren't in the auction, and they're almost always described in terms of points.
Can anyone explain how a cooperative game can value ranks over points? I don't see a way.
In a cooperative game that values ranks, players form a cartel. Everyone is ranked 1st place in all attributes with 96 points left over. It's an optimal strategy for a cooperative group -- no penalty for getting first place cheaply, no need to be better than your teammates. I used to worry about that but I've realized that I absolutely do not have cooperative players. I have players that get excited and leave the lower ranks in the dust. Even when the PCs are best friends, the players still have bloodthristy bidding wars.
I think TonyLB described the optimal strategies in competetive bidding wars, but I'd like to destablize the case where no one can outbid 3rd place.